As the nature of my curious profession requires me to use as many cartridges as possible, I did a lot of hunting with the 7mm Remington Magnum and the .300 Winchester Magnum, and tried very hard to like them. But it didn't work out. Both have the same virtue and the same fault. The virtue is that they are somewhat more powerful than standard cartridges of the same caliber, and their fault is that they are somewhat more powerful than standard cartridges of the same caliber.
The 7mm Remington was probably inspired by the Mashburn 7mm Magnum, which Warren Page brought to fame over his 25 years as shooting editor of Field & Stream -- except the Mashburn was a lot more powerful than the Remington round. Warren pushed a 175-grain bullet at just over 3,000 fps from his rifle, which the Remington will not do in any way, shape, or form. The .300 Winchester had to follow in the giant footsteps of the .300 Weatherby, which is much longer, and does everything in a much bigger way.
The 7mm Remington kicks considerably more than a .270 or a .280, and has a bit more effective range, but not much. Similarly, the .300 Win Mag has bigger numbers than a .30/06, but not much. But it kicks noticeably harder. I had several rifles in both calibers in the 1970s and 1980s, and used them hard, but I finally gave up on them and went to non-magnum rounds instead. My shoulder is happier, the animals fall down just as fast, and I do not miss these rifles at all.